We do the symmetry game at group time in the spring (my mother used to do this with me when I was really young, yay memories!) Many of my three year olds are now four and are beginning to grasp larger concepts. We talk about the wings of a butterfly when we introduce symmetry aka bilateral symmetry. I will draw a butterfly on the chalkboard as guided by the children narrating my process as I do so. Then I place an object on one side and invite a child to match it on the other side. Once everyone gets a turn, we place more chalkboards on the carpet for the children to play it together. It's totally cool if they do not get it, they will someday. What this does is give us teachers a chance to assess the children without assessing them. Sometimes, there will be a child so into the game that it carries off into their play for the week. They discover other items with smmetry and we guide them through their learning based o nwhere their interests are.